>Hi,
>I am being asked to develop an application to run on a Windows tablet running Windows 8 or Windows 10 Professional.
>I guess I can install SQL Express, but would like to use the version with the smallest footprint. Can anyone tell me what that would be? SQL Server Compact? LocalDB? Something else?

SQL Compact has the smallest footprint by far. But I would probably try to go with SQL Server 2008 R2, because it gives you a full SQL Server with SP, advanced tools etc, but that depends on your needs. In any case using SQL Server 2008 would mean your solution is easily scalable.

SQL Server 2008 R2 requires 512 MB RAM, SQL Server 2010 requires already 4GB RAM.

Here the requirements for SQL 2008 R2:

Supported Operating System
Windows 7, Windows Server 2003, Windows Server 2008, Windows Server 2008 R2, Windows Vista, Windows XP

System Memory:
Minimum 512 MB for SQL Server Express with Tools, and SQL Server Express with Advanced Services and 4 GB for Reporting Services that installs with SQL Server Express with Advanced Services

Hard Disk:
2.2 GB of Disk Space

Processors:
X86:
Pentium III-compatible processor or faster (Processor Speed - 1.0 GHz or faster)

X64:
Minimum: AMD Opteron, AMD Athlon 64, Intel Xeon with Intel EM64T support, Intel Pentium IV with EM64T support (Processor Speed - 1.0 GHz or faster)

IA64:
Itanium processor or faster (Processor Speed - 1.0 GHz or faster)
Limitations : SQL Server Express supports 1 physical processor, 1 GB memory, and 10 GB storage